The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem

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• 作者：Jiangxing Wang ; Chuanmiao Chen ; Ziqing Xie
• 关键词：Averaging discontinuous Galerkin method ; Two point boundary values problem ; Superconvergence ; Green function
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：70
• 期：1
• 页码：175-191
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree k, the numerical flux convergence at a rate of \(2k+2\) for all mesh nodes (in particular, the numerical flux for \(k=0\) has the second order superconvergence rate). Numerical experiments are shown to demonstrate the theoretical results.